A Contingent-Claims Approach to the Inventory-Stocking Decision

Abstract

This paper presents option-pricing solutions to the inventory-stocking problem when demand is distributed discretely or continuously. The model readily incorporates inventory salvage values and stockout costs, and shows that option-pricing models can be used to determine the optimal stocking levels. The contingent-claims approach is a straightforward extension of the traditional inventory framework, and allows the technology of financial economics to be applied to this important class of assets. The conventional approach to inventory decisions relies on an expected profit-maximization criterion, which takes as its starting point a distribution of demand for the inventory item. The starting point for the contingent-claims approach presented here is to associate the demand for an inventory item to the price of an underlying state variable. Inventory payoffs depend on demand and the quantity stocked as well as the selling price, salvage value, and penalties for stockouts. To apply the contingent-claims approach, we construct a portfolio of options that replicates these inventory payoffs, value the portfolio, and then subtract the inventory investment to establish the net present value (NPV) of an inventory policy.